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#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

Lex Fridman Podcast vor 8 Monaten

0:00

Joel David Hamkins is a mathematician and philosopher
specializing in set theory, the foundations of mathematics, and
the nature of infinity, and he’s the #1 highest-rated user on
MathOverflow. He is also the author of several books, including
Proof and the Art of Mathematics and Lectures on the Philosophy
of Mathematics. And he has a great blog called Infinitely
More.

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Transcript:

https://lexfridman.com/joel-david-hamkins-transcript

CONTACT LEX:

Feedback – give feedback to Lex:
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AMA – submit questions, videos or call-in:
https://lexfridman.com/ama

Hiring – join our team:
https://lexfridman.com/hiring

Other – other ways to get in touch:
https://lexfridman.com/contact

EPISODE LINKS:

Joel’s X: https://x.com/JDHamkins

Joel’s Website: https://jdh.hamkins.org

Joel’s Substack: https://www.infinitelymore.xyz

Joel’s MathOverflow:
https://mathoverflow.net/users/1946/joel-david-hamkins

Joel’s Papers: https://jdh.hamkins.org/publications

Joel’s Books:

Lectures on the Philosophy of Mathematics:
https://amzn.to/3MThaAt

Proof and the Art of Mathematics: https://amzn.to/3YACc9A

SPONSORS:

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OUTLINE:

(00:00) – Introduction

(01:58) – Sponsors, Comments, and Reflections

(15:40) – Infinity & paradoxes

(1:02:50) – Russell’s paradox

(1:15:57) – Gödel’s incompleteness theorems

(1:33:28) – Truth vs proof

(1:44:52) – The Halting Problem

(2:00:45) – Does infinity exist?

(2:18:19) – MathOverflow

(2:22:12) – The Continuum Hypothesis

(2:31:58) – Hardest problems in mathematics

(2:41:25) – Mathematical multiverse

(3:00:18) – Surreal numbers

(3:10:55) – Conway’s Game of Life

(3:13:11) – Computability theory

(3:23:04) – P vs NP

(3:26:21) – Greatest mathematicians in history

(3:40:05) – Infinite chess

(3:58:24) – Most beautiful idea in mathematics